My theory is that changing the direction of the line along which these masses are traveling requires work.

Is this a personal theory or have you made some inquiries, say, of the literature to find out what is actually happening?

Most flying insects have two pairs of wings - flys have one.
Where you'd normally find the second pair, the fly has a pair of stubs called "halters".
They don't work the way you seem to be expecting, but it's hard to tell. iirc they provide a kind of gyroscopic stability but also act as sensitive turn-rate sensors.